Numerical Solution of Advection-Diffusion Equation Using Preconditionar as Incomplete LU Decomposition and the BiCGSTAB Aceleration Method

TL;DR

This paper presents a numerical approach for solving the advection-diffusion equation using ILU preconditioning and BiCGSTAB acceleration, comparing different discretization schemes and boundary conditions for improved solution efficiency.

Contribution

It introduces the application of ILU preconditioned BiCGSTAB method to advection-diffusion problems with various boundary conditions and discretization schemes.

Findings

ILU preconditioning improves convergence

Centered scheme yields accurate results

Method effective for Dirichlet and Neumann conditions

Abstract

In the present study, an advection-diffusion problem has been considered for the numerical solution. The continuum equation is discretized using both upwind and centered scheme. The linear system is solved using the ILU preconditioned BiCGSTAB method. Both Dirichlet and Neumann boundary condition has been considered. The obtained results have been compared for different cases.